STRUCTURE 



137 



6.0 



(0 



4.0 - 



cr 



2.0 



0.2 0.4 0.6 



Concentration g/IOOcc 



Figure 6-7. Determination of Molecular Weight 

 of Collagen by Osmotic Pressure (7r) Measure- 

 ments. The intercept at c = is equal to 1/M n . 



through a derivation due to Einstein and Debye. The resulting expression 

 relates the intensity of the light scattered (R w ) at right angles (90°) to the 

 incident light and the concentration of the scatterer in solution: 



Kc_ 

 R 



90 



M " M 2 



where A" is a constant depending upon the wavelength of the incoming light, 

 the index of refraction of the solvent, and other factors, all of which can be 

 measured. A plot of Kc/R 90 vs c, then, has an intercept (value at c = 0) of 

 1/M, the reciprocal of which is the weight-average molecular weight. 



Sedimentation Equilibrium. Perhaps the most versatile of them all, this 

 method of measuring molecular weight can give a reliable value indepen- 

 dently (almost) of the shape. 



In the ultracentrifuge, which spins so rapidly that the centrifugal force 

 can be higher even than 100,000 times that of the gravitational attraction 

 to the earth when the suspension is at rest, a macromolecule can reach a 

 stable position at which the centrifugal force is exacly balanced by a force in 

 the opposite direction which is proportional to the number of buffeting mole- 

 cules per cc (Brownian motion). Heavy molecules come to equilibrium at a 

 position near the bottom of the centrifuge tube, light molecules toward the 

 top. 



After the solution has spun long enough for the macromolecules to assume 

 their equilibrium distribution (usually some days for big molecules), the 

 concentration, c, and concentration gradient dc/dx along the linear axis, x, 

 of the tube (measured from the center of rotation), are measured, usually by 

 a light-refraction technique. Use of the expression 



(1 - p)u 2 xc \_ B 

 RT dc/dx MM 2 



c + 



